Quantum information processing promises to perform some significant tasks far more efficiently than can be accomplished classically. Important examples of possible applications include quantum computation, quantum simulation, and quantum communication. Physical systems of various kinds are under consideration for quantum information processing. Trapped atomic ions constitute one such physical system and they are, in fact, a promising physical qubit candidate for developing quantum computation.
Individual qubits are defined in the trapped atomic ion system by isolating two quantized energy levels of the ion's configuration. Different states can include configurations of various properties of the atomic electron and nucleus such as electron orbit, electron spin, and nuclear spin. However, since the state of the electron is always involved, it is convenient to refer to them as electronic states and transitions between them as electronic transitions. These quantum electronic states can be separated by energy differences corresponding to electromagnetic excitation from radio frequencies (RF) to optical wavelengths. Controlled electronic transitions are performed by applying excitation pulses of electromagnetic fields at the corresponding frequency (or equivalently, wavelength).
There are two important types of operations carried out in quantum information processing with trapped ions. Manipulation of an individual ion to control its electronic quantum state configuration, as mentioned above, is known as a single qubit rotation. This term refers to the mathematical rotation of the quantum state vector in the Bloch-sphere representation and is analogous to the rotation of the spin vector in Nuclear Magnetic Resonance (NMR).
Additionally, trapped ions can be made sufficiently cold (i.e. their motion sufficiently suppressed by, for instance, laser cooling) so that the state of their motion may also be described quantum mechanically. Ion motion is then described by quantized levels of excitation (energy levels) of a quantum harmonic oscillator. Using excitation pulses tuned to the electronic transition plus or minus the harmonic-oscillator energy level spacing, changes in the ion's electronic state configuration can be coupled to changes in its amount of harmonic oscillator motional excitation, either increasing or decreasing its motional energy. With single or multiple qubits, excitation of these motional modes requires significant electromagnetic field gradients on the scale of the ion motion, which is typically on the order of 10 nm.
For quantum information processing, it is necessary to interact ions together in order to perform processing operations with the information stored in the different qubits, similar to performing logic operations with different bits in a classical computer.
The primary means of doing this is to trap ions together in a linear chain, so that they are separated by, and interact through, their electrostatic (Coulomb) repulsion. Then, instead of single ion harmonic oscillator motional excitations, there are collective modes of oscillation for all of the ions.
Two simple examples of collective modes are: (1) the center of mass (COM) mode for two ions, where the ions move jointly side to side, and (2) the stretch mode, where the ions oscillate towards and away from each other. By tuning excitation pulses to an ion's electronic state transition plus or minus the oscillation mode energy level spacing, changes in an ion's electronic state configuration are coupled to changes in the amount of motional excitation in that mode. Because this excitation involves other ions, exciting their motion as well, the overall (electronic+motional) quantum states of the various ions interact and their quantum states become entangled.
Because of this entanglement, the occurrence of a quantum transition involving multiple ions in response to an electromagnetic pulse can be made conditional on the initial states of the qubits, thus enabling quantum logic operations. Controlled interactions of this sort between qubits are the second operation necessary to perform quantum information processing and are known as multi-qubit gates, analogous to gate operations with multiple bits in classical computation.
To date, qubit rotations and gates are performed primarily with tightly focused laser beams. This is done either with direct excitation of electronic energy levels separated by energies corresponding to optical wavelengths (optical qubits) or indirectly with simulated Raman transitions, where two laser beams are applied at wavelengths that are separated by the required transition frequency.
Raman transitions are normally used to stimulate transitions between electronic states defined by the hyperfine interaction between the atomic nucleus and the electron in odd-isotope atoms (i.e. atoms with net nuclear spin). This interaction causes an energy splitting of the electronic ground state into multiple levels which are separated by energies corresponding to microwave frequencies. These qubits are commonly known as hyperfine qubits or, alternatively, clock states because of their widespread use in atomic-clock applications.
Most current schemes for quantum information processing with trapped ions use laser-induced interactions to implement the necessary qubit rotations and gates with one-dimensional chains of trapped ions. Whereas laser-based schemes have been successful in manipulating small numbers of ions, scaling up to larger register sizes and/or multiple quantum registers will demand a large overhead in laser-beam power and control. Additionally, multi-qubit gates rely on the ability to spectrally isolate a single motional mode of an ion chain. Because there are 3N modes of motion for N trapped ions, increasing N to large values can make the mode spectrum so dense that the gate speeds must be significantly reduced to avoid off-resonant coupling to other modes. Reduction of gate speeds is highly detrimental to quantum computing because decoherence of the qubits in time limits the fidelity of the operations. As a result, large numbers of qubits must be dedicated to performing error correction, thus escalating critical system resource requirements.
The alternative to one-dimensional ion chains is to distribute the ion qubits in an array of multiple trap zones. In that architecture, gate operations can be carried out on a relatively small number of ions in multiple processing zones. Interactions are facilitated by physically moving the ions to different zones for different operations in a “quantum CCD bus” architecture, analogous to movement of charges on a solid-state CCD image sensor. Yet even there, optical qubits require laser beams to be applied in several locations simultaneously for parallel operations. Moreover, spontaneous emission and technical difficulties associated with stabilizing laser frequency, phase, amplitude, and beam pointing have kept optical qubit gate fidelities below fault-tolerant levels and are likely to remain a limiting factor for some time.
The shortcomings of lasers for qubit operations can be overcome by using, instead, microwave magnetic fields to directly manipulate hyperfine qubits. These clock states are commonly used for atomic frequency standards because they are highly stable; they are practically immune to decoherence by spontaneous emission, and they are readily addressed by highly stable, commercial-off-the-shelf (COTS) microwave sources.
To date, the advantages of using microwave magnetic fields have not been realized because for free-space microwaves, their long wavelength precludes focusing, causing all qubits to be simultaneously addressed, and because only negligible field gradients can be produced on the ion-motion scale, precluding coupling to motional modes.
To overcome these issues, microfabricated ion traps offer a solution: microwave electrodes with sub-wavelength dimensions can localize fields to individually address subsets of qubits and generate sufficient magnetic field gradients to excite entangling motional modes.
A practical quantum-information processor based on microwave manipulation of qubits will need to have electromagnetically isolated regions where qubit preparations and interactions are accomplished with microwave fields delivered with on-chip waveguides. To achieve this, progress is needed in integrating high magnetic field gradients and microwaves on-chip with effective field localization. This will involve relatively high current densities to provide sufficient field strengths and field gradients. Progress is also needed in shielding or cancelling of microwave fields from other zones to minimize unintentional qubit manipulations due to crosstalk.
Integrated microwave addressing in ion traps offers a physical implementation for future quantum information processing systems. Addressing the hyperfine states of specific trapped ions to achieve single-qubit and two-qubit rotations using microwaves instead of lasers has the potential to reduce the quantity and required purity of lasers required for these operations, potentially reducing the complexity and improving the fidelity of quantum information processing.
Because of the large physical wavelength of the microwave signal relative to the ion, integration into the structure of the ion trap is required to achieve localized near-field coupling of the microwave magnetic field with the ion. Generally, single-qubit and two-qubit operations require two different field profiles at the ion location: a uniform microwave magnetic field density for single-qubit operations, and a microwave magnetic field with zero magnitude and a high gradient for two-qubit operations.
Prior efforts to integrate microwave electrodes into microfabricated ion traps have demonstrated both single-qubit and two-qubit operations with good fidelity. NIST has demonstrated single-qubit gates with <10−4 error using beryllium (9Be+) ions addressed at 1.25 GHz, individual addressing of magnesium (25Mg+) ions using field gradients at 1.687 GHz, and entangled Mg qubits addressed at 1.69 GHz. These results have been achieved with a microfabricated ion trap consisting of a single layer of thick (8-11 μm) gold traces on quartz or aluminum nitride (AlN) substrates, offering both high current handling capability and low microwave loss, and good thermal management in the AlN case.
The University of Oxford has reported single-qubit operations with good fidelity using calcium (43Ca+) ions addressed using three microwave wires at 3.2 GHz, with proposals for more complex electrode designs to allow addressing and correction at neighboring sites.
GTRI reports single-qubit rotations in 171Yb+ addressed at 12.6 GHz using a trap with two 1 μm-thick aluminum (Al) coplanar waveguides separated from an Al ground plane on a silicon substrate by 10 μm of silicon dioxide (SiO2) dielectric. Additional relevant work includes traps with integrated electrodes that carry DC currents to generate static magnetic field gradients.
Although progress has been made, it has proven challenging, for several reasons, to integrate microwave electrodes with a microfabricated ion trap. First, the characteristic dimensions of the integrated microwave “antennas” are similar to those of the RF and control electrodes that are used to position the ion in space above the trap, requiring co-location of the microwave structures with the rest of the ion traps. Second, the on-chip traces, as well as the feed to the trap, must have sufficient frequency range and bandwidth to deliver the microwave signals efficiently from the microwave source to the coupling structures. Finally, high field gradient operation requires high microwave currents, requiring larger conductor cross-sections and good thermal management.